Of all the enemies Batman has faced down, none have tested his mettle, his endurance, and his sanity the way the Joker has. He seemed to step fully-formed from the darkest part of the caped crusader's own psyche, transcending the line between a mortal ally, and a force of pure madness that must be contained. Behind the facade of the Clown Prince of Crime, though, is the Joker really as mad as we think he is? Or is there a method to even the most ridiculous and dangerous of his ploys and plans? If you'd like to answer some of those questions at your Pathfinder table, here's a guide to help you get started.
The Character Conversions page on Improved Initiative has more character builds, including the Dark Knight himself, if you're interested.
Attributes, Race, and Traits
As far as we know, the Joker is human. Not only that, but we know he's brilliant, extraordinarily tough, capable of acrobatic feats you wouldn't think possible, and that he's significantly stronger than he appears. He also has a force of personality that can fill a room, and leave an impression on anyone who sees him. Put in game terms, you should prioritize his Intelligence, without neglecting his physical stats, or dumping his Charisma into single-digit numbers.
When it comes to his traits, it's important to pick options that are both thematically appropriate, and which give the character bonuses which are going to come into play often enough to make a difference. For example, Unpredictable provides a +1 trait bonus on Bluff checks, but if you're not going to use the Bluff skill with your version of the character then the trait isn't terribly helpful. Bruising Intellect could easily represent the intense dressing-down he gives his henchmen in many of the classic comics, since it allows you to use your Intelligence modifier for making Intimidate checks, but it isn't helpful if you won't be using the Intimidate skill. Surprise Weapon, which grants a +2 bonus on attacks with improvised weapons, is great if you're re-enacting the crowbar scene from when the Joker killed Jason Todd, but you need to ask if it's going to be part of your regular schtick before you spend your trait slot on it.
Alchemical Prodigy, which increases your alchemist level by 1 when it comes to the expiration time of your extracts, is a good investment. Along with Wicked Leader, which gives you a +2 trait bonus in dealing with evil outsiders, but significantly bigger bonuses if you take the feat Vile Leadership.
While the Joker has had a lot of incarnations over the life of the character, most of his methods have remained the same. The trappings of the clown, from his acid-spraying flower to his shocking joy-buzzer have come and gone, but what has remained is his reliance on explosives, gas-based weapons, and particularly, deadly poisons. Even his origin story, never truly set, features him falling into a vat of chemicals and being horribly scarred by them, resulting in his bizarre appearance.
All of these features are something you can easily make with an Alchemist. However, which aspects of the Joker's development over the years will influence which Discoveries you invest in. For example, the most obvious two to invest in are smoke bomb and poison bomb, which would allow for the noxious green vapors the character is so associated with. Some players might want to homage The Dark Knight's version of the character with the delayed bomb and implant bomb Discoveries, which would allow you to implant a bomb into a willing or helpless creature, which will then detonate in 24 hours. For players who want to play up the character's use of corrosive weapons, the acid bomb Discovery is a good one to have, whereas a madness bomb could be a thematic way to represent the chemical insanity the Joker often leaves in his wake.
Extracts might seem like something that doesn't fit this character, but ask yourself how many times you've seen the Joker pull out a vial of something or other as an ace up his sleeve? Something to counteract a poison, cure a disease, or make him appear dead for a time so he can get out of Arkham with no one the wiser? These and dozens of other examples are the Joker's edge over a lot of his victims, as well as his nemesis. Also, remember, an Alchemist can prepare extracts as he needs them. He doesn't have to ready them all in the beginning of the day if he doesn't want to.
In addition to gaining poison use, and the ability to quickly and easily manufacture alchemical items, there is one more thing. You know, the thing that doesn't quite fit. Why keep the Mutagen class feature for the Joker?
Well, while it isn't thematically a part of his character, it would support certain actions we've seen in his stories. For example, how many villains do you know that are strong enough to knock Batman out with a sucker punch? Or tough enough to take a full-force beating from one of Gotham's Knights, then get back up while still laughing and swinging a crowbar? While not technically the result of any superhuman powers, the Joker's physicality seems to fluctuate dramatically, which could be explained by use of mutagens.
Also, it should be noted that if you want to bump your damage, increase your skills, and maybe get your hands on evasion, a two-level dip in Rogue is never a bad idea. Especially since it would give you access to a lot of class skills you don't have, that you could use.
Skills and Feats
Alchemists get a lot of skills. As to what we've seen the Joker use, well, there are a lot of options to choose from. Craft (Alchemy) is top of the list, but Sleight of Hand and Disable Device should also make your list. Heal is a good skill to add, as is Perception. Since we're in a fantasy game, Knowledge (Arcana) and Use Magic Device can also come in quite handy. And if you have leftover ranks, Intimidate, Diplomacy, and Sense Motive can all be useful, along with Knowledge (Local).
Now, on to your feats!
The Joker is not a combat heavy. Sure, he puts up a good fight, but his major strength lies in his ability to plan, to develop just the right weapon, and to make the site of his ambush really count. When he does mix it up, he typically starts at range, or taking pot shots to wear down his foes. So, you're going to want Point Blank Shot and Precise Shot (Core Rulebook 131). It's also a good idea to invest in Skill Focus (134) if you're planning on making a certain skill your character's bread and butter. And if there's anyone who should have Endurance and Die Hard (Core Rulebook 122), it's the man who spends days in solitary confinement without losing any strength, and then proceeds to have his skull fractured and teeth knocked out by a billionaire vigilante.
There is, however, one feat that is something quintessentially Joker. That feat is Vile Leadership, from Champions of Corruption. Someone possessing this feat has a gang of cowed followers, and an evil cohort, but the bonuses and negatives are nearly the inverse of what you'd find taking the regular Leadership feat. For example, if you gain bonuses for being ruthless, and you gain more bonuses for punishing followers to keep others in line (like when the Joker pushed a too-curious underling in front of a truck, and kept on walking while whistling a jaunty tune). Tolerance for failure, lethargy, and indecision, on the other hand, all make you look weak, and negatively impact how many followers you have doing your bidding.
Which answers the major question everyone has always had... how the hell does the Joker, an avowed mass-murdering psychopath, keep finding mooks to support his crazy plans?
Equipment and Story
The Joker is a character who takes whatever he has lying around, and turns it into what he needs. He has no signature equipment, barring some of his recurring themes like the joy buzzer, flower, and playing cards. You'd be better off, though, with a hand crossbow (or a revolver with a ridiculously long barrel, if you're willing to spend that kind of gold and eat a feat to use firearms for an homage) and a number of knives hidden on your person. With all that said, though, you might want to peruse The Best Alchemical Items For Your Pathfinder Party to make sure you're using all the best toys to your advantage. Of course, a spring-loaded wrist sheathe can go a long way toward delivering a poisoned stab, or putting a vial of something noxious in your hand at just the right moment.
As to your story, you have a lot of wiggle room regarding who your Joker is, and where he comes from. For example, is he a madman run loose in Galt, aiding this faction one day, and then blowing them up the next, instituting his own chaotic element into the fractured nation's political whirlpool? Did he fall into one of the refuse pools in Nex, crawling out of the alchemical sludge with a head full of vapors and a hair-trigger laugh? Or did he get his scars in Nidal, where he underwent part of the Joymaking ritual, but escaped, naming himself the Joymaker, and gathering a horde of dark jesters to make those who would deny the Midnight Lord scream with laughter... or just plain scream?